A double white dwarf with a paradoxical origin?

We present Hubble Space Telescope UV spectra of the 4.6-h-period double white dwarf SDSS J125733.63+542850.5. Combined with Sloan Digital Sky Survey optical data, these reveal that the massive white dwarf (secondary) has an effective temperature T-2 = 13 030 +/- 70 +/- 150 K and a surface gravity log g(2) = 8.73 +/- 0.05 +/- 0.05 (statistical and systematic uncertainties, respectively), leading to amass of M-2 = 1.06 M-circle dot. The temperature of the extremely low-mass white dwarf (primary) is substantially lower at T-1 = 6400 +/- 37 +/- 50 K, while its surface gravity is poorly constrained by the data. The relative flux contribution of the two white dwarfs across the spectrum provides a radius ratio of R-1/R-2 similar or equal to 4.2, which, together with evolutionary models, allows us to calculate the cooling ages. The secondary massive white dwarf has a cooling age of similar to 1 Gyr, while that of the primary low-mass white dwarf is likely to be much longer, possibly greater than or similar to 5 Gyr, depending on its mass and the strength of chemical diffusion. These results unexpectedly suggest that the low-mass white dwarf formed long before the massive white dwarf, a puzzling discovery which poses a paradox for binary evolution.